I think it would work better with a slight twist: set a reasonable score floor, run a lottery for everyone above it. Instead of giving the world to people who(se parents have paid to) optimize their studies to a particular test, everyone who proves a certain degree of capability has a chance. Students simply do their best, and fate and the RNG takes care of the rest. If it becomes a problem, that we're underserving too many bright and promising youth because too few are getting into Ivies under this regime... maybe create more Ivy-likes (Stanford says hi).

And for anyone who thinks it's unfair: not anymore so than the parent lottery. And I think institutional acknowledgment of the role pure dumb luck plays in our lives would go a long way towards dispelling our inclination to actively punish people for acts of the cosmos and/or dysfunctional policy.